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Quarter and core the apples and cut into smallish dice – a bit smaller than canned pineapple cubes. Put half the butter in a frying pan (you will need a lid for it later), heat until foaming, then tip in the apples. Fry for 7-10 minutes, turning more or less constantly, until golden brown all over and just tender when prodded with a knife. Lift out and set aside.
Melt the remaining butter in the pan and fry the chopped shallots for 2-3 minutes. Move them to the sides of the pan so they don’t start to burn, then put the chicken in, skin side down. Cook the chicken, without moving it, for 3-4 minutes until browned, then turn it over and cook in the same way for another 3-4 minutes.
Heat about one third of the calvados in a ladle or small pan. Remove from the heat and set light to it with a match, then pour it over the chicken in the pan, stirring to burn off the fat. Repeat with the remaining calvados, in two batches.
Pour in the stock and season with salt and pepper. Cover and simmer very gently for 15 minutes or until the chicken is cooked and tender. Lift the chicken on to a board and set aside to rest for a few minutes.
Vigorously bubble the remaining juices in the uncovered pan for a couple of minutes, to reduce, then stir in the apples and crème fraîche and keep the pan over a low heat.
Carve each breast thickly into 6 or 7 diagonal slices and transfer them to warmed plates, keeping the slices together by lifting them with a fish slice or wide palette knife. Check the seasoning of the sauce and spike with a touch of lemon juice, then spoon over the chicken. Sprinkle with parsley and eat.